Carbine was designed to replace the .45 pistol for troops whose main job (artillerymen, signalers, drivers,etc) made carring a full sized rifle too difficult. There was a definite weight limit and length limit in the original specification.

There are a lot of fun "what if" posts in the aircraft section, I ASSumed one would be appropriate here too.
Guess not.

The point is to explore the possibility if the operating mechanism design that developed into what was to be called the M1 carbine could have formed the basis of what came to be called an assault rifle.

Perhaps there is no way, regardless of how it was scaled up, the mechanism could have fulfilled this roll.
Or perhaps yes.

Bigger rounds within reason are welcome. I don't mean 416 Rigby as an upper limit.
But carbines and firepower was answered by men i have known that would discard anything they were carrying to pick up m2 carbines on the battlefield whenever they could.

Perhaps a bit more enthusiasm in the defense of the "what if" and it might bait folks. Whatcha think?

You are talking about a round with half again as much energy. The intent of the M1 carbine was to give a rifle to an untrained user. Size was very important. So as soon as you start increasing barrel length, adding compensators, and beefing up the breach/bolt area to handle the extra stress... you are quickly creating a different animal that likely would not have matched the original premise.

Also of note is that the 30 Remington was yet another cartridge whose deveopment was made for lever action carbines where round nose bullets were required. Therefore, you are buying additional power, but not much range. Sure you can put a pointy thing in the case, but you can't exceed OAL. For if you did it wouldn't be a .30 Remington now would it. Thus you would have to load fairly light FMJBT and with the need to keep them short in length, ballistic coefficient would similarly suffer.

As stated already, the .30 Carbine is basically a pistol replacement. Unfortunately it looked like a rifle so people used it like one and thus gave it a bad reputation. At one point, I believe prototypes were chambered for something resembling a .223 Remington and it functioned well enough. Now THAT would be a good "Light Rifle" / Assault Rifle. The problem here though is that because of its design (check the way it is held together), the accuracy is severly limited.